In the field of image guidance, registration is the quantification of the transformation between two or more coordinate systems. After successful registration, the position of a tool or other object in one coordinate system, such as an optically tracked space, can be accurately displayed in another coordinate system, such as the medical image space. In the case where image guidance or robot-assisted image guidance is to be performed using a preoperative 3D image dataset such as a computed tomography (CT) scan or magnetic resonance imaging (MRI) scan, co-registration among multiple coordinate systems may be needed, such as between a preoperatively obtained anatomical CT or MRI coordinate system, an intraoperatively obtained anatomical coordinate system, a coordinate system of the tracking cameras, and the like.
One way to achieve co-registration of multiple coordinate systems is to use 2D-3D registration, such as where a pair of 2D x-ray radiographs of the patient is taken at the time of surgery, with the position of the x-ray machine and patient tracked using tracking cameras. The coordinate system in which the x-rays are taken may then be registered to a preoperatively obtained 3D medical image coordinate system through methods of 2D-3D registration. In this method, the 3D CT or MRI dataset may be used to generate 2D reconstructed planar images simulating x-ray radiographs. One way to generate 2D reconstructed simulated x-ray images from a 3D dataset is to trace and integrate the intensities along rays from a point source projected through the volumetric medical image on a 2D plane (e.g., a digitally reconstructed radiograph (DRR)). The DRRs are generated iteratively until they match the actual 2D x-ray images; that is, until the features or intensity characteristics of the bone structures on the DRRs and actual radiographs overlap within some tolerance. For instance, the iterative method could be a method such as Powell's Method, by which a cost function is minimized by starting with a guess and then adjusting parameters systematically until the error is within tolerance. As an example, the cost function could be constructed by subtracting the pixel intensities at locations within the images in the DRRs and the actual x-ray radiographs, and would be minimized when the pixel intensities agreed closest between X-ray and DRR in both views of the x-ray pair. Parameters of the cost function that could be adjusted between iterations may include the position and orientation of the 3D volumetric data, the x-ray source, angles of x-ray paths relative to the 3D volume, and the like, varied independently and/or simultaneously within the known (tracked) geometric constraint of the actual relative positions of the x-ray machine when the pair of shots were taken. Once a match is found, the position in the CT or MM coordinate system in which the x-ray machine must have been at the time the x-rays were taken is known from the parameters used in the calculation. Also, the position of the actual x-ray machine in the tracking coordinate system is known from tracking cameras. Therefore, the transformations between CT (or MRI), x-ray, and camera coordinate systems are determined.
Iterative methods as mentioned above, however, may be problematic because a large number of iterations may be required before a successful match is found. This may result in a long time delay, or worse, the iterations may fail to converge on a solution. Therefore, systems and methods are needed to improve the convergence of 2D-3D registration.